Question

Select the correct answer from each drop-down menu.

Point C(3.6, -0.4) divides in the ratio 3 : 2. If the coordinates of A are (-6, 5), the coordinates of point B are ____
If point D divides in the ratio 4 : 5, the coordinates of point D are ____
(fraction)

Answer 1

B is (10, -4), and D is (58/9, -2)

Explanation:

Answer 2

Coordinates of point B are (10,-4)

Coordinates of point D are (3.6,-0.4)

Explanation:

1) Point C(3.6, -0.4) divides in the ratio 3 : 2. If the coordinates of A are (-6, 5), the coordinates of point B are ____

Let the coordinates of B be
`(x_2,y_2)`

Coordinates of A =
`(x_1,y_1)=(-6,5)`

Coordinates of C=(x,y)=(3.6,-0.4)

We will use section formula over here

`x=(mx_2+nx_1)/(m+n) , y = (my_2+ny_1)/(m+n)`

m:n=3:2

`3.6=(3x_2+2(-6))/(3+2) , -0.4=(3y_2+2(5))/(3+2)3.6 * 5 = 3x_2-12, -0.4 * 5 = 3y_2+10\\18+12=3x_2 , -2=3y_2+10\\30=3x_2 , -12=3y_2\\10=x_2, -4=y_2\\`

Coordinates of B = (10,-4)

2)If point D divides in the ratio 4 : 5, the coordinates of point D are ____

(fraction)

Let the coordinates of D be
`(x,y)`

Coordinates of A =
`(x_1,y_1)=(-6,5)`

Coordinates of B=
`(x_2,y_2)=(10,-4)`

We will use section formula over here

`x=(mx_2+nx_1)/(m+n) , y = (my_2+ny_1)/(m+n)`

m:n=3:2

`x=(3(10)+2(-6))/(3+2) , y=(3(-4)+2(5))/(3+2)\\x=3.6,y=-0.4`

Coordinates of point B are (10,-4)

Coordinates of point D are (3.6,-0.4)